When Federal Reserve Chairwoman Janet Yellen presented her semiannual testimony to Congress in February the jobless rate was 6.7% and annual inflation was 1.2%. When she returns for two days of testimony Tuesday and Wednesday, she will have a 6.1% jobless rate and 1.8% inflation to report to lawmakers.

What matters most in her testimony will be how she explains these developments, particularly the job market’s improvement.

A lower unemployment rate and inflation closer to the Fed’s 2% objective is good news for the economy. It suggests the economy weathered a first quarter slump in economic output without losing job market momentum or veering further from the Fed’s inflation goal. It also poses Ms. Yellen with a challenge.

The jobless rate is falling much faster than officials expected. A year ago at this time officials projected the jobless rate wouldn’t get close to 6% until late 2015. Ms. Yellen has said the Fed’s plans for interest rates depend on how fast the economy converges on its goals of maximum employment and 2% inflation. A slow path to those goals implies a long delay before the Fed’s benchmark short-term rate rises from near zero and a fast path to those goals implies a quicker takeoff.

Some regional Fed bank presidents have argued of late that the rapid descent in unemployment argues for the latter.

“Unemployment has surprised to the downside,” James Bullard, president of the Federal Reserve Bank of St. Louis, said in an interview with The Wall Street Journal last week. Most Fed officials don’t expect to raise interest rates until 2015. Mr. Bullard is calling for rate increases by the first quarter of 2015, sooner than many other officials, and said he might want rate increases even sooner if economy growth picks up in the next few months.

Ms. Yellen argued in her February testimony that the Fed can’t put too much weight on the unemployment rate because slack in the labor market remains hidden in other forms. For example, 7.5 million workers have part-time jobs but want full-time work. That is up from 7.2 million in February, though down from 8.2 million a year ago. The jobless rate also has fallen in part because some individuals have retired or stopped looking for jobs, effectively removing themselves from measures of unemployment.

“While conditions in the labor market have improved appreciably, they are still far from satisfactory,” Ms. Yellen said in an update on the economy to the Joint Economic Committee in May.

Will she stick to this line or offer a rosier assessment of the job market after a five-month stretch in which businesses have added 1.2 million positions to their payrolls? The answer will set the tone for her whole testimony. A rosier view would imply an earlier liftoff for rates.

The job market discussion sets the stage for Ms. Yellen to address a related conundrum. The job market is improving even though economic growth has been dismal. Output fell at a 2.9% annual rate in the first quarter and was up just 1.5% from a year earlier, well short of the 3% growth rates officials have been anticipating for years. Officials believe bad weather set the economy back in the first quarter and that output is rebounding. Yet the long-run growth rate shows no sign of accelerating.

Why is the job market improving and growth not? Ms. Yellen’s answer – if she is asked – has important implications for interest rates in the near-run and long-run. One possible explanation is that workforce productivity isn’t growing very fast, damaged perhaps by the financial crisis or business under-investment. That might explain why businesses need more workers to deliver small increases in growth. If that’s the case, slack in the job market might be diminishing sooner than Fed officials expected.

For now Fed officials appear largely unworried about the recent pickup in inflation statistics. Many of them believed the low measures recorded last year were driven by special factors, like government cuts in Medicare payments. Wage increases have been modest for the most part. It would take a sustained lift in inflation measures to convince many officials that consumer price increases are returning to the Fed’s 2% goal sooner than expected.

Ms. Yellen testifies before the Senate Banking Committee Tuesday, starting at 10 a.m., and the House Financial Services Committee Wednesday at 10 a.m.

In her February testimony she also spent a substantial amount of time discussing financial conditions, an issue that appears likely to come up again this week. She said in a June press conference and a recent speech to the International Monetary Fund that she is watching closely for signs of froth and market complacency, but isn’t yet worried enough about market developments to alter the Fed’s interest rate plans.

About Real Time Economics

Real Time Economics offers exclusive news, analysis and commentary on the U.S. and global economy, central bank policy and economics. Send news items, comments and questions to the editors and reporters below or email realtimeeconomics@wsj.com.